Communications terminal and operating method

ABSTRACT

A non-coherent technique employs a zero padded FFT for the fast acquisition of direct sequence spread spectrum signals in the presence of large Doppler shifts. The application of a FFT to code acquisition results in decreased acquisition time, and can improve the probability of detection. A set of partial correlators ( 1 ) and a zero padded FFT ( 2 ) are used to reduce the search region for code acquisition while maintaining good frequency resolution for Doppler offset. This approach will prove most pertinent in future reconfigurable terminals.

BACKGROUND OF THE INVENTION

The present invention relates to a communications terminal and a methodof operating a communications terminal.

The inflexibility of frequency division multiple access and timedivision multiple access techniques has resulted in the development ofnew systems based on the uncoordinated spread spectrum concept. In thesenew systems, the bits of slow speed data traffic from each subscriberare multiplied by a high chip rate spreading code, forcing each low bitrate (narrowband) data signal to fill a wide channel bandwidth. Manysubscribers can then be accessed by allocating a unique, orthogonalspreading code to each. This constitutes a code division multiple access(CDMA) system. In the receiving terminal, the desired signal is detectedby correlation against a local reference code which is identical to theparticular spread spectrum code employed prior to transmission.

Rapid initial code acquisition and re-acquisition is crucial in CDMAcommunications. DOPPLER or local oscillator offsets can lead tofrequency uncertainty which make this task particularly difficult.Existing strategies for code acquisition are single and multiple dwelldetectors, matched filters, sequential detection and parallel detectors.In the presence of frequency uncertainty, the most common approach is tosequentially search all code phases over the range of anticipatedfrequency offsets. This brute force approach is laborious and can leadto large acquisition times.

Current second generation mobile communication systems cannot providesufficient capacity to support the future demands of increasedsubscribers and higher data rates for multimedia communications. Thirdgeneration systems will be required to provide multiple access schemeswhich are capable of flexible data rates and variable services. However,it will considerably aid the acceptance of third generation systems ifexisting standards, infrastructures and components can be reused orreconfigured.

One common way of acquiring a direct sequence spread spectrum (DS-SS)signal is through the use of an energy detector at the output of thedespreader. This approach works by tuning the code phase and frequencyoffset of a complex matched filter over the range of possible phase andfrequency offsets anticipated in the system. When the phase of thedesired spreading sequence (usually measured in terms of code chips) andlocal oscillator frequency offset are within specified limits, thedetector will produce an output which exceeds some threshold and thesystem will register the presence of the desired user. This initialacquisition will then trigger a verification loop which confirms thepresence of the desired code sequence and subsequently a tracking loopwhich attempts to continuously maintain close alignment between the twocode sequences in order to track any fluctuations. If the desiredspreading sequence phase and frequency offset are not within the limits,the output of the detector will not exceed the threshold, and the searchfor initial acquisition will continue.

The number of possible search bins will be determined by the product ofthe number of possible code phase offsets (typically a half chip searchis employed over the entire sequence), and the total range of possibleDoppler offsets. The width of each Doppler bin is in turn determined bythe frequency response of the complex correlator, thus yielding a2-dimensional search plane as depicted in FIG. 1. The acquisition cellssystem sequentially searches this grid by aligning the reference codephase and frequency offset to the centre of each cell. The time requiredin order to obtain an initial acquisition will therefore depend directlyon the number of cells in the search region. For systems with longspreading codes, which might experience large Doppler offsets, thisacquisition time may prove prohibitively large.

We will consider, for example, a system with random codes of length 200,in which the range of possible Doppler shifts is +/−32 kHz. Thenormalised frequency response of a complex matched filter (MF) is afunction of the Doppler frequency offset Δf, as given below.$\begin{matrix}{{{H\left( {\Delta\quad f} \right)}} = {\frac{1}{M}\frac{\sin\left( {M\quad{\pi\Delta}\quad{fT}_{c}} \right)}{\sin\left( {{\pi\Delta}\quad{fT}_{c}} \right)}}} & (1)\end{matrix}$

In (1), M is the length of the spreading code, Δf is the Dopplerfrequency offset and T_(c) is the chip duration. FIG. 2 depicts thefrequency response of a complex MF for a data rate of 8 kHz (M=200,T_(c)=625 ns). We see that the 3 dB bandwidth of the complex MF withthese parameters is around 4 kHz. This will result in a total of(200×2)×(64/4)=6400 cells which the energy detector must search. It hastherefore been proposed, for example in Sust et al, “Rapid AcquisitionConcepts for Voice Activated CDMA Communication” IEEE Globecom 90, pp1820-1828, and in Stirling-Gallacher et al “A Fast Acquisition Techniquefor a Direct Spread Signal in the Presence of a Large Doppler Shift”IEEE ISSSTA 96, pp 156-160, to introduce a FFT based improvement to theenergy detector which will reduce the number of possible cells byevaluating a reduced search space.

By re-examining FIG. 1, it would be possible to substantially reduce theacquisition time, if it were possible to search all possible codeDoppler cells simultaneously. By employing a FFT block as part of theacquisition system it would be possible to perform this form of searchprocedure. A block diagram of such a FFT enhanced acquisition system isshown in FIG. 3.

The system consists of P complex matched filter correlators 1, each oflength X, such that the product X×P equals the code length M. The firstcorrelator will contain the first X chips of the spreading sequence, thesecond will contain the next X chips, and so on through the Pcorrelators. The outputs of the P correlators are therefore partialcorrelation results. These partial results are then passed to a N-pointFFT 2, where N=P. The processing gain of this receiver is the same asthe original energy detector, however if the correlator length X ischosen correctly, the addition of FFT processing allows the simultaneoussearch of all possible code Doppler shifts.

A specific example should illustrate this more effectively. Continuingwith the previous example, where M=200 and T_(c) =625 ns, in order toincrease the bandwidth of the partial correlators to beyond +/−32 kHz,their length is decreased to X=25. Therefore the number of partialcorrelators is P=8. If N=P i.e. a 8-point FFT is selected, FIG. 4depicts the output of a maximum signal selector superimposed on all theFFT bin outputs. The bandwidth of the FFT processor has increased, andis much improved over the standard complex correlator. To furtherincrease the bandwidth, the length of the individual correlators shouldbe reduced and the total number of correlators increasedcorrespondingly.

This FFT enhancement will allow all possible code Doppler offsets to besearched simultaneously. However, a scalloping loss can be observed whenthe Doppler offset falls between two bins of the FFT. This will resultin a reduced probability of detection for signals with these Doppleroffsets, as compared to signals which occur in the centre of any givenbin.

SUMMARY OF THE INVENTION

The present invention seeks to improve the acquisition time of a spreadspectrum communication system, preferably through the reuse of FFTprocessing blocks. The approach taken is thought to be particularlyapplicable to third generation mobile systems, for which reuse and/orreconfiguration of hardware will be an important priority.

According to one aspect of the invention there is provided acommunications terminal for use in a code division multiple accesssystem, comprising a plurality of correlating means, each forcorrelating a part of a spreading code sequence relating to a signal tobe acquired, and zero padded Fast Fourier Transform (FFT) means foroperating on the output of the correlating means. The inclusion of azero padded FFT increases the resolution of the FFT processor withoutincreasing the overall bandwidth.

Preferably, the correlating means each comprise a complex matched filtercorrelator and preferably each correlator is of the same chip length,the product of the chip length of each correlator and the number ofcorrelators being equal to the code length. Good results are obtained ifthe chip length of each correlator is 25 or less.

Preferably, the terminal includes a hard limiter at the input to thecorrelating means. This enables the use of cheap digital correlators.

The FFT means may in particular be a complex zero padded FFT processorwhich preferably has at least twice as many points as the number ofcorrelators and may have four or eight times as many. The output of theFFT means may be supplied to a maximum signal selector for signalacquisition.

According to another aspect of the invention there is provided a methodof operating a code division multiple access communications terminal soas (to acquire a given signal, comprising correlating the spreading codesequence of the given signal in a plurality of partial correlationoperations, and processing the partial correlation results using a zeropadded Fast Fourier Transform (FFT).

Preferably, prior to the correlation step, the signal is passed througha hard limiter, and preferably, after the FFT step, the maximum signalpresent is selected to acquire the given signal.

The invention utilises a FFT to simultaneously search all possible codeDoppler offsets at one time, thus reducing the 2-dimensional searchproblem to a 1-dimensional search for code phase. By zero padding theFFT increased frequency accuracy is provided, which ensures that desiredsignals with Doppler offsets which lie between two bins of the FFT arenot masked.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described in more detail, by way ofexample only, with reference to the accompanying drawings, in which:

FIG. 1 is a diagram showing the search region for a conventional CDMAenergy detector acquisition system;

FIG. 2 shows the frequency response of a complex matched filtercorrelator;

FIG. 3 is a block circuit diagram of an FFT based acquisition systemsadapted from that of Sust et al;

FIG. 4 shows the output of the system shown in FIG. 3;

FIG. 5 shows the output of a system according to an embodiment of theinvention;

FIG. 6 is a graph of probability of false alarm in the system of FIG. 3and in embodiments of the invention;

FIG. 7 is a graph of probability of detection in the system of FIG. 3;

FIG. 8 is a graph as FIG. 7, but also relating to embodiments of theinvention; and

FIGS. 9 and 10 are graphs of mean acquisition time in the system of FIG.3 and in an embodiment of the invention, for two different respectivefalse alarm penalty values.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 5 shows the response when a 16-point FFT is inserted in the systemshown in FIG. 3, with the maximum signal selector superimposed. Thenumber of correlators P=8, and their length X=25, remain unchanged. Itcan be seen that effectively there are more FFT output lobes in the samerange of Doppler frequency uncertainty and therefore the scalloping lossis reduced.

In order to quantify the difference this padding effects, consider asignal with a Doppler offset of 28 kHz. This lies directly between twobins of the 8-point FFT shown in FIG. 4. The normalised magnituderesponse at this offset is approximately 0.46. However, when the16-point padded FFT (FIG. 5) is employed the normalised responseincreases to approximately 0.7. It is clear that further levels ofpadding will further reduce the scalloping loss which occurs, howeverthe rate of improvement decreases rapidly with increasing amounts ofpadding. For this scheme it is apparent that no further increase will beseen above a 64-point FFT.

The approach discussed above is an improvement of the swivellingcorrelator described by Sust et al. In Sust et al, the inclusion of FFTprocessing was seen as an additional burden on the processor, andtherefore the FFT was kept as small as possible. Implementing a largeFFT will not necessarily present such a problem in third generationterminals.

The earlier discussion neglected the impact of the hard limiter 3 whichis placed at the input of the correlators. This has the effect ofconstraining the input to the first correlator to be either +/−1. Thiscauses the statistics of the signal at the input to the correlators tobe binomial, and when no signal is present this limiter constrains thevariance of the noise. If the interference statistics can be assumed tobe Gaussian, the hard limiter will result in a loss of approximately 2dB. The simulation results presented below confirm this. In lightlyloaded CDMA channels the interference statistics cannot be assumed to beGaussian, and this loss will probably increase further. A worst case washighlighted by Sust et al, in which there are only two users withunbalanced power. The limiter will have the effect of suppressing theweaker user, although receiver dither can be successfully used to combatthis problem.

Despite these limitations, the limiter 3 is still attractive from adigital signal processing perspective. The use of hard limiting allowssingle bit quantisation, and therefore cheap digital correlators can beemployed as opposed to more costly analogue or high resolution digitalprocessors. The simulation results presented herein include the impactof the hard limiter, however the more detailed problems highlighted inthe above paragraph are not considered.

In order to quantify the possible improvements which can be gained byemploying a padded FFT, some approximate theoretical expressions for theperformance of the FFT based acquisition system are derived below. Inparticular, three performance measures are considered: false alarmprobability, probability of detection and mean acquisition time.

A. Probability of False Alarm.

In this section, the probability of false alarm, P_(fa), is derived,assuming that the desired signal is not present. The false alarmprobability will depend upon the statistics of the noise at the input tothe detector, and upon the threshold level employed in the detector. Asa result of the limiter at the input to the correlators, the noise willhave a binomial distribution, with unit variance and zero mean. If thecorrelators are assumed to be sufficiently long, the central limittheorem can be applied to show that the signals at the input to the FFTare uncorrelated and have Gaussian statistics. If each correlator is oflength X, then each output will have variance X and mean zero. If thereare P correlators, then the outputs of a zero padded N-pt FFT (i.e. N>P)will have variance PX(=M, the code length) and zero mean. The magnitudeof the outputs of the FFT are used in the detector—these amplitudesignals will be Rayleigh distributed with probability density function(pdf) given by $\begin{matrix}{{p(r)} = {\frac{r}{M}{\mathbb{e}}^{\frac{- r^{2}}{2M}}}} & (2)\end{matrix}$and cumulative distribution function (cdf) $\begin{matrix}{{F(r)} = {1 - {\mathbb{e}}^{\frac{- r^{2}}{2M}}}} & (3)\end{matrix}$

The probability that any one FFT output is greater than some thresholdlevel t, is given by $\begin{matrix}{{P\left\lbrack {{output} > t} \right\rbrack} = {\mathbb{e}}^{\frac{- r^{2}}{2M}}} & (4)\end{matrix}$

All of the FFT outputs have the same distribution, and therefore theprobability of any one of the N outputs exceeding the threshold (andhence the probability of false alarm) is given simply by $\begin{matrix}{P_{fa} = {1 - \left( {1 - {\mathbb{e}}^{\frac{- r^{2}}{3M}}} \right)^{N}}} & (5)\end{matrix}$B. Probability of Detection.

The derivation of the probability of detection follows that of the falsealarm probability. In this case it is assumed that the desired signaland corrupting noise are present at the input to the acquisition system.Again the noise at the inputs to the FFT is assumed to be decorrelatedand Gaussian with variance X and mean zero. If the mean desired signallevel at the input to the acquisition system is X, then the mean signallevel (in bin 0 at frequency 0 Hz) will be PXα=Mα. The output noisevariance is M as before. At the output of the FFT, the amplitudes of thesignals are taken, thus the statistics of the output of some FFT bin iare Rician, with pdf given by $\begin{matrix}{{p_{i}(r)} = {\frac{r}{M}{\mathbb{e}}^{- {(\frac{r^{2} + s_{i}^{2}}{2M})}}{I_{0}\left( \frac{{rs}_{i}}{M} \right)}}} & (6)\end{matrix}$where I_(o) is the zero-th order modified Bessel function, and S_(i) isthe summation of the mean of the signals on the inphase and quadraturebranches for bin i,S _(i) ² =m _(I) ² +m _(Q) ²  (7)

The cumulative distribution function of the Rice distribution is givenby $\begin{matrix}{{F(r)} = {1 - {{\mathbb{e}}^{- {(\frac{r^{2} + s_{i}^{2}}{2M})}}{\sum\limits_{m = 0}^{\infty}\quad{\left( \frac{s_{i}}{r} \right)^{m}{I_{m}\left( \frac{{rs}_{i}}{M} \right)}}}}}} & (8)\end{matrix}$

The probability that the amplitude of bin i is greater than somethreshold t is given by $\begin{matrix}{{P^{i}\left\lbrack {{output} > t} \right\rbrack} = {{\mathbb{e}}^{- {(\frac{r^{2} + s_{i}^{2}}{2M})}}{\sum\limits_{m = 0}^{\infty}\quad{\left( \frac{s_{i}}{r} \right)^{m}{I_{m}\left( \frac{{rs}_{i}}{M} \right)}}}}} & (9)\end{matrix}$

Signal acquisition is assumed if any of the output bins is greater thanthe threshold. Each of the N FFT output bins has the same distribution,and therefore the probability of any one of the N outputs exceeding thethreshold (and hence the probability of detection) will be given byP _(d)=1−P _(no detection)  (10)$\begin{matrix}{P_{d} = {1 - {\prod\limits_{i = 0}^{N}\quad\left( {1 - {P^{i}\left\lbrack {{output} > t} \right\rbrack}} \right)}}} & (11)\end{matrix}$C. Mean Acquisition Time.

The present analysis considers a single dwell detector. The acquisitionmodel can be summarised as follows. Suppose there are q cells to besearched (through a combination of both code phase and Doppleruncertainty). Assume that if a hit is detected (i.e. the magnitude ofany output of the FFT is greater than some threshold), the system goesinto a verification mode that may include an extended dwell period and acode tracking loop period. The false alarm penalty of entering theverification mode when the desired signal is not present is modelled asKτ_(d), where the dwell or integration time is given by τ_(d). The meanacquisition time for such a single dwell system has been derived as$\begin{matrix}{{\overset{\_}{T}}_{acq} = {\frac{\left( {2 - P_{d}} \right)\quad\left( {1 + {KP}_{fa}} \right)}{2P_{d}}\left( {g\quad\tau_{d}} \right)}} & (12)\end{matrix}$

In order to aid comparison between different systems, the meanacquisition time is often normalised to the integration time T_(d) asfollows $\begin{matrix}{\frac{{\overset{\_}{T}}_{acq}}{\tau_{d}} = {\frac{\left( {2 - P_{d}} \right)\quad\left( {1 + {KP}_{fa}} \right)}{2P_{d}}(q)}} & (13)\end{matrix}$

The mean acquisition time results presented below use values of P_(fa)and P_(d) derived from simulation, for a selection of false alarmpenalty values.

The theoretical performance of the FFT acquisition scheme of theinvention is now compared with Monte Carlo simulation results. Thesimulations investigate the effect of using increasingly larger paddedFFTs on the three variables for which the theoretical values werederived above. For simplicity and consistency, the same systemparameters are used as in the previous examples. To recap, a data rateof 8 kHz is assumed, with random codes of length M=200 which leads to achip period of 625 ns. The partial correlators are of length X=25, whichmeans that there are 8 inphase and quadrature inputs to the FFT block.The received sequence with the carrier offset of 28 kHz which washighlighted earlier is also considered below. This will clearlyillustrate the improvement achieved by zero padding in the FFT.

A. False Alarm Probability.

The first set of results concerns the probability of false alarm. FIG. 6presents the results from Monte Carlo simulation of four different FFTsizes. The acquisition system was simulated with only noise present, andthe simulation was terminated when either the equivalent of 1 milliondata bits had been transmitted, or 500 false alarm errors werecollected.

The dotted lines in FIG. 6 depict the theoretical false alarmprobability as computed by (5) against the threshold level in thedetector. It is apparent that increasing the FFT size results in anincrease in the probability of false alarm, since with more output binsthere is an increased probability of any one individual bin exceedingthe threshold. The theoretical curves assume that each of the N outputbins of the FFT are independent and equally likely to exceed thethreshold. However, there are only 8 non-zero and independent inputs tothe FFT, which means that the output bins will not be truly independent.This effect is seen in the “saturation” observed in the simulatedpoints—as the FFT size is successively increased the false alarmprobability quickly reaches a maximum value. It will become apparentfrom the next set of results that it is possible to compensate for theincreased probability of false alarm by improving the probability ofdetection.

B. Probability of Detection.

The theoretical probability of detection can be computed from (11)through the Markum Q function. A Q function evaluation algorithm wasused to evaluate the theoretical curves for FIGS. 7 and 8. The Markum Qfunction is the infinite sum in (11), i.e. $\begin{matrix}{{Q\left( {\frac{S_{i}}{\sigma},\frac{t}{\sigma}} \right)} = {{\mathbb{e}}^{- {(\frac{r^{2} + s_{i}^{2}}{2M})}}{\sum\limits_{m = 0}^{\infty}\quad{\left( \frac{s_{i}}{r} \right)^{m}{I_{m}\left( \frac{{rs}_{i}}{M} \right)}}}}} & (14)\end{matrix}$

The algorithm computes the value of Q(•, •) by using a truncated seriesapproximation. FIG. 7 compares the theoretical and simulated values ofprobability of detection for an 8 point FFT for three threshold valuesat a Doppler offset of 28 kHz. The graph shows that as the thresholdvalue is decreased the probability of detection is increased, andthat asthe signal-to-noise ratio (SNR) increases the probability of detectionalso increases.

It is also possible to see the impact of hard limiting on theperformance of the detector. The limiter quantises the received signalinto either +/−1 values, so that the individual outputs of the partialcorrelators have integer, rather than real values. Therefore, therotating phasors which are observed at the partial correlator outputsare quantised in value, rather than following their theoreticallycontinuous pattern. Provided the correlators are sufficiently long, andthe noise is dominant, this quantisation error will be small. WhenGaussian noise corrupts the input to a hard limiter, it has the effectof linearising the limiter's operating characteristic. At higher SNRvalues, the characteristic is more nonlinear (when no noise is input thelimiter characteristic is extremely nonlinear), so that the impact ofthe quantisation is only seen at higher SNR values. The theoreticalcurves, shown dotted in FIG. 7, do not include the operation of thelimiter to illustrate the loss in performance due to this quantisationerror.

The next set of results considers the improvement which can be achievedby zero padding the FFT to increase the frequency resolution. FIG. 8contrasts four FFT sizes, for a detection threshold of 60. As waspredicted, the probability of detection increases as the FFT sizeincreases. However, a similar saturation effect can be seen as wasobserved in the false alarm probability results. This occurs because thetheoretical curves assume that each output bin of the FFT has an equalprobability of containing the desired signal, however the outputs of apadded FFT are weakly dependent and this is evidenced in the lack ofimprovement in the detection probability above FFT sizes of around 64.Despite this saturation effect, the addition of zero—padding to the FFThas improved the probability of detection by a factor of approximately3. Again, the Doppler offset is 28 kHz and the dotted theoretical curvesneglect the effect of hard limiting.

C. Mean Acquisition Time.

The mean acquisition results use (13) with values for P_(d) and P_(fa)derived from the earlier simulation studies. The results presented hereconsider the two false alarm penalty values, K=1, 50. These valuesrepresent two different extremes, and so help to illustrate thedependence between the increased false alarm rate and improvedprobability of detection.

FIGS. 9 and 10 depict the mean acquisition time as a function of SNR,with K=1 and K=50, respectively. It is apparent that the use of thelarger (padded) FFT results in a decrease in the mean acquisition timefor both false alarm penalty values. The improvement is most dramaticfor higher threshold values. With a detection threshold of 60 and K=1,the mean acquisition time for the 64 point FFT is approximately onethird that of the 8 point FFT. However, for a threshold of 40 with K=50there is little difference in mean acquisition time between the two FFTsizes. FIG. 10 shows that at high SNR values it would be preferable toimpose a larger detection threshold, since the large value of falsealarm penalty makes false alarms more dominant in the acquisition time.

The present invention thus provides an improved acquisition scheme fordirect sequence spread spectrum communications. The technique reuses FFThardware available from other functions to simultaneously search allcode Doppler offsets, and thereby reduce the mean acquisition time. Thereuse of hardware (for example OFDM receiver hardware) in a mannersimilar to this will prove vital to the success of future thirdgeneration communication terminals.

When the code Doppler shift of the desired sequence falls between twobins of the FFT, zero padding of the FFT block can lead to reductions inthe acquisition time. Zero padding results in a slight increase in thefalse alarm probability, however this is compensated for by an increasein the probability of detection.

The method of the invention holds promise for implementation in futurereconfigurable terminals in mobile and satellite communications systems.

1. A communications terminal for use in a code division multiple accesssystem, comprising a plurality of correlating means, each forcorrelating a part of a spreading code sequence relating to a signal tobe acquired, and zero padded Fast Fourier Transform (FFT) means foroperating on the output of the correlating means, wherein the FFT meansoperates on the output of the correlating means to enable differentpossible frequency offsets to be simultaneously analyzed, and whereinthe FFT means operates on the output of the correlating means to enablethe different possible frequency offsets to be simultaneously analyzedto enable selection of Doppler offset for a selected output.
 2. Acommunications terminal according to claim 1, wherein the correlatingmeans each comprise a complex matched filter correlator.
 3. Acommunications terminal according to claim 2, wherein each correlator isof the same chip length and wherein the product of the chip length ofeach correlator and the number of correlators defines the length of thespreading code.
 4. A communications terminal according to claim 3,wherein the chip length of each correlator is 25 or less.
 5. Acommunications terminal according to claims 1, 2, 3 or 4, including ahard limiter at the input to the correlating means.
 6. A communicationsterminal according to claims 1, 2, 3 or 4, wherein the FFT meansincludes a complex zero padded FFT processor having at least twice asmany points as the number of correlating means.
 7. A communicationsterminal according to claim 6, wherein the FFT processor has four timesas many points as the number of correlating means.
 8. A communicationsterminal according to claim 6, wherein the FFT processor has eight timesas many points as the number of correlating means.
 9. A communicationsterminal according to claim 6, wherein the output of the FFT means issupplied to a maximum signal selector for signal acquisition.
 10. Amethod of operating a code division multiple access communicationsterminal so as to acquire a given signal, comprising: correlating thespreading code sequence of the given signal in a plurality of partialcorrelation operations; processing the partial correlation results usinga zero padded Fast Fourier Transform (FFT), wherein the partialcorrelation results are processed using a zero padded FFT to enabledifferent possible frequency offsets to be simultaneously analyzed; andAnalyzing the different possible frequency offsets simultaneously toenable selection of a Doppler offset for a selected output.
 11. A methodaccording to claim 10, wherein, prior to the correlation step, thesignal is passed through a hard limiter.
 12. A method according to claim10 or 11, wherein, after the FFT step, the maximum signal present isselected to acquire the given signal.